W4-DQs Correlations & Regressions

What does the symbol n ? Xi

i 1

mean ? provide an example

The above symbol means the SUM of X 's values , where values are n

For example , if there 7 number as 3 , 5 , 2 , 7 , 9 , 4 , 6

Then

7 ? Xi 3 5 2 7 9 4 6 36

i 1

The following sample observations were randomly selected

X : 4 , 5 , 3 , 6 , 10

Y : 4 , 6 , 5 , 7 , 7

Determine the coefficient of correlation and the coefficient of determination . Interpret the results

Using

EXCEL

The coefficient of correlation 0 .7522

The coefficient of determination 0 .5659

X and Y are positively correlated

X explains ' 56 .59 percent of the variation in Y

The following sample observations were randomly selected

X : 5 , 3 , 6 , 3 , 4 , 4 , 6 , 8

Y : 13 , 15 , 7 , 12 , 13 , 11 , 9 , 5

Determine the regression equation

Determine the value of Y ' when X is 7 Using EXCEL

Slope - 1 .74

Intercept 19 .12

The regression equation : Y - 1 .74X 19 .12

Y - 1 .74 7 19 .12 6 .94

The following regression equation was computed from a sample of 20 observations

Y 15 - 5X

SSE was found to be 100 and SST Determine the standard error of estimate

Determine the coefficient of determination

Determine the coefficient of correlation (Caution : Watch the sign

SST SSR SSE

SSR 400 - 100 300

The standard error of estimate Square root of [SSE (n-2 )] Square root of [100 (20-2 )] Square root of [100 /18] 2 .357

The coefficient of determination SSR /SST 300 /400 0 .75

The coefficient of correlation Square root of the coefficient of determination - 0 .866

The correlation coefficient is negative because there is a negative trend given by regression equation (slope - 5...